1 citations · 1 across the 3 of their papers we have counts for
4 papers
Weak and strong interaction of excitation kinks in scalar parabolic equations
Antoine Pauthier, Jens D. M. Rademacher, Dennis Ulbrich
Motivated by studies of the Greenberg-Hastings cellular automata (GHCA) as a caricature of excitable systems, in this paper we study kink-antikink dynamics in the perhaps simplest…
Large-time behavior of solutions of parabolic equations on the real line with convergent initial data II: equal limits at infinity
Antoine Pauthier, Peter Poláčik
We continue our study of bounded solutions of the semilinear parabolic equation on the real line, where is a locally Lipschitz function on Assum…
Advection-diffusion dynamics with nonlinear boundary flux as a model for crystal growth
Antoine Pauthier, Arnd Scheel
We analyze the effect of nonlinear boundary conditions on an advection-diffusion equation on the half-line. Our model is inspired by models for crystal growth where diffusion model…
Road-field reaction-diffusion system: a new threshold for long range exchanges
Antoine Pauthier
We consider reaction-diffusion equations of KPP type in a presence of a line of fast diffusion with non-local exchange terms between the line and the framework. Our study deals wit…